What is the Greatest Common Factor of 65744 and 65749?

Greatest common factor (GCF) of 65744 and 65749 is 1.

GCF(65744,65749) = 1

We will now calculate the prime factors of 65744 and 65749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65744 and 65749.

How to find the GCF of 65744 and 65749?

We will first find the prime factorization of 65744 and 65749. After we will calculate the factors of 65744 and 65749 and find the biggest common factor number .

Step-1: Prime Factorization of 65744

Prime factors of 65744 are 2, 7, 587. Prime factorization of 65744 in exponential form is:

65744 = 2⁴ × 7¹ × 587¹

Step-2: Prime Factorization of 65749

Prime factors of 65749 are 37, 1777. Prime factorization of 65749 in exponential form is:

65749 = 37¹ × 1777¹

Step-3: Factors of 65744

List of positive integer factors of 65744 that divides 65744 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 587, 1174, 2348, 4109, 4696, 8218, 9392, 16436, 32872

Step-4: Factors of 65749

List of positive integer factors of 65749 that divides 65744 without a remainder.

1, 37, 1777

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65744 and 65749. The biggest common factor number is the GCF number.
So the greatest common factor 65744 and 65749 is 1.

Also check out the Least Common Multiple of 65744 and 65749